Question

circle j is congruent to circle p. if ok = 2x, qr = 12, and rt = x + 3, what is the length of chord km? 8 9 10 12

Explanation:

Step1: Use congruent - circle property

Since circle J is congruent to circle P, corresponding chords are equal. Chords OK and RT are corresponding chords, so \(OK = RT\).

Step2: Set up the equation

We know that \(OK = 2x\) and \(RT=x + 3\), so \(2x=x + 3\).

Step3: Solve the equation for x

Subtract x from both sides: \(2x−x=x + 3−x\), we get \(x = 3\).

Step4: Find the length of chord KM

Chords KM and QR are corresponding chords in congruent circles, so \(KM=QR\). Given \(QR = 12\), so \(KM = 12\).

Answer:

12